If a + b + c = 0, then the value of \frac{a^2+b^2+c^2}{a^2-bc} is:

Algebra and Applications Test 3

Question : 13 of 25

Marks: +1, -0

If a + b + c = 0, then the value of

{a^2+b^2+c^2}/{a^2-bc}

is:

Solution:

a + b + c = 0

⇒ b + c = -a

Squaring on both sides, we get:

⇒ b^2 + c^2 + 2bc = + a^2

Adding a2 on both sides, we get:

⇒ a^2 + b^2 + c^2 + 2bc = 2a^2

a^2 + b^2 + c^2 = 2a^2 - 2bc

= 2(a^2 - bc)

∴{a^2+b^2+c^2}/{a^2-bc}={2(a^2-bc)}/{a^2-bc}=2

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